In general, do I need to treat water in NZ?

You may not need to treat, but filtered water from a stagnant tarn tastes a lot better. Same for water without particles.

Sawyer products are great. Buy in the US first because in NZ they're likely to cost more than the GDP of several small countries. https://sawyer.com/products/?type=water-filtration Tramped down the Whakatane in Te Urewera a couple of years ago. Heard a rumour about a certain hut having a possum in the water tank. Unlike me, my mate insists on filtering all water so I obliged him. Next morning we peered into the tank and sure enough there was a possum carcass at the bottom of the tank. Let's just say the local community didn't appreciate visitors. Ditto for all the points raised before my post. Nothing beats beautiful NZ water from a mountain stream. I've never got sick but I am also vigilant in assessment. A stream is almost always better than a water tank at a hut.

As has been the general observation - I've not treated water in NZ. However, like most here, I tramp in areas that don't drain farmland. I have drunk from tanks, tarns (big and small) and streams. NZ has a very high flux of rain water so concentrations of biological contaminants (E coli for example) are low. The only 'precaution' I take is, if downstream of a hut, I prefer to take water from a side stream rather than the river.

Going back to school days I remember tramping in Fiordland. Never took a water bottle but instead you just plunged your hands into the moss on the side of the track let them fill up and drink. Strong earthy flavours reminiscent of a very oaky shiraz but it never harmed anyone

If you are wary of Giardia, take water from near the surface of a still-ish patch of river. Giardia is heavier than water and sinks. Turbulence stirs it up. Avoid river sediment particles. As Waynowski alluded, any water that hasn't been through farmland is probably good - at least in the South Island. I prefer to boil my hut water. https://www.wildernessmag.co.nz/boil-toil-trouble/

I have had some interesting tasting hut water before but never boiled it. Huts with coal fires get a strong ashy taste. Also seen various critters in the tank when leaving the hut still no issue. Closest Ive got to boiling hut water is thawing out a lump

A local microbiologist did a survey of Arthurs Pass National Park water and only found giardia in the catchment of Temple Basin Skifield which at that time was popular with Canadian snowboarders. Giardia doesn't stay in our environment longer than 18 months because we don't have the right vectors to maintain it e.g. beavers. Our animals have giardia but not the nasty form of it. So to be on the safe side in areas popular with overseas folk, I would choose a side stream and go up it a bit beyond the possible toileting zone. So far so good. Blue Lake Hut had a carcass problem a couple of years ago and the Te Araroa people were suffering from it.

I picked up a nasty dose of giardia (properly diagnosed) in the 80's. But it was 100% my own stupid fault; farmland and lots of people camping on it. Otherwise I've never had the slightest problem with any stream water arising from forested or mountain terrain. There may be a risk, but in my opinion it's low.

A portion of ash from everything that's burned in the wood burner ends up in the hut water tank. Everything burned, plastics, aluminium, etc. will create ash some of which will end up in the tank. That's why some hut tank water tastes smoky. And I don't know about you, but I love having burned plastic and aluminium coursing through my veins. It feels like... victory...

The ash has nothing to do with the smoke taste. It's the filtration method.